Error of confounding cause and effect.There is no more dangerous error than confounding consequence with cause: I call it the intrinsic depravity of reason. I take an
example: everybody knows the book of the celebrated Comaro, in which he recommends his spare diet as a recipe for a long and happy life,for a virtuous life also. Few books have been read so much I believe hardly any book has caused so much harm, has shortened so many lives, as this well-meant curiosity. The source of this mischief is in confounding consequence with cause. The candid Italian saw in his diet the cause of his long life, while the prerequisite to long life, the extraordinary slowness of the metabolic process, small consumption, was the cause of his spare diet. He was not at liberty to eat little or much; his frugalitywas not of free will; he became sick when he ate more.

Every teacher certainly should know something of non-euclidean geometry. Thus, it forms one of the few parts of mathematics which, at least in scattered catch-words, is talked about in wide circles, so that any teacher may be asked about it at any moment. ... Imagine a teacher of physics who is unable to say anything about Röntgen rays, or about radium. A teacher of mathematics who could give no answer to questions about non-euclidean geometry would not make a better impression.On the other hand, I should like to advise emphatically against bringing non-euclidean into regular school instruction (i.e., beyond occasional suggestions, upon inquiry by interested pupils), as enthusiasts are always recommending. Let us be satisfied if the preceding advice is followed and if the pupils learn to really understand euclidean geometry. After all, it is in order for the teacher to know a little more than the average pupil.

Socrates: Shall we set down astronomy among the objects of study?
Glaucon: I think so, to know something about the seasons, the months and the years is of use for military purposes, as well as for agriculture and for navigation.
Socrates: It amuses me to see how afraid you are, lest the common herd of people should accuse you of recommending useless studies.

Building goes on briskly at the therapeutic Tower of Babel; what one recommends another condemns; what one gives in large doses another scarce dares to prescribe in small doses; and what one vaunts as a novelty another thinks not worth rescuing from merited oblivion. All is confusion, contradiction, inconceivable chaos. Every country, every place, almost every doctor, have their own pet remedies, without which they imagine their patients can not be cured; and all this changes every year, aye every mouth.

In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion.
(1987) -- Carl Sagan